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Math is the Language of Chemistry! Explore Scientific Notation and Metric Conversions

Discover how scientists use scientific notation to express large and small numbers. Learn about converting metric measurements and significant figures in chemistry calculations. Practice rounding and applying dimensional analysis using conversion factors. Join the journey through this engaging tutorial!

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Math is the Language of Chemistry! Explore Scientific Notation and Metric Conversions

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  1. MATH IS THE LANGUAGE OF CHEMISTRY!!!

  2. Scientific Notation Scientist use special notation to expressvery largeorvery smallnumbers. Example I: 300,000,000 m/sec can be written as… 3 x 108 m/sec Ex II: 1,007,000,000 sec can be written as… 1.007 x 109 sec Ex III: 0.000 000 000 004 76 m can be written as… 4.76 x 10-12 m

  3. Converting Metric Measurements(PART 4 of Things to Know and Love) To convert, move the decimal place the number of stairs you step on in the direction you are traveling OR use dimensional analysis. kilo- 103 hecto- 102 deca- basic unit 101 1 deci- Example: 3.75 km = ? mm 10-1 centi- 10-2 milli- ? = 3,750,000 mm 10-3

  4. SIGNIFICANT FIGURES • Scientists indicate the precision of measurements by the number of digits they report = sig. figs. • A value of 3.52 g is more precise than a value of 3.5 g • All known digits plus one estimated digit ** the equipment used for a measurement will determine the number of sig. figs.

  5. Significant Figures Atlantic - Pacific Rule: Decimal Present: Count from the Pacific side Decimal Absent: Count from the Atlantic side Start counting at the first non-zero number and count until you reach the end of the number Ex. I: 3.00700 Decimal Present… Pacific (left)… 6 sig. figs. Ex. II: 300,700 Decimal Absent… Atlantic (right)… 4 sig. figs. (the last 2 zeros are PLACE HOLDERS)

  6. REVIEW Determine how many significant figures are in each of the following measurements. • 0.0034050 L ___________ • 33.600 m ___________ • 7500.0 g ___________ • 47,900 mm ___________ • 7,000,000,001 miles ___________ • 8.07 Hz ___________ 5 (the first 3 zeros are PLACE HOLDERS) 5 5 3 (the last 2 zeros are PLACE HOLDERS) 10 3

  7. More practice… Round the following measurements off so that they each contain 3 significant figures. • 366.2 L ___________ • 9,047,022 mg ___________ • 12.76 g ___________ • 999.9 J ___________ 366 L 9,050,000 mg 12.8 g 1.00 x 103 J Notice this one must be in scientific notation to have 3 sig. figs.

  8. Significant Figures in Calculations When multiplying and dividing, limit and round to the least number of significant figures in any of the factors. Example: 23.0 x 432 x 19 = 188,784 = 190,000 The answer is expressed as 190,000 or 1.9 x 105 since 19 has only two sig. figs.

  9. Significant Figures in Calculations When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers involved in the calculation. Example: 123.25 + 46.0 +86.257 = 255.507 = 255.5 The answer is expressed as 255.5 since 46.0 has only one decimal place.

  10. REVIEW Perform the prescribed operations. Round your answers to the proper # of sig. figs. • 36.57 m / 3.21 s = ___________ • 41.376g + 13.3g + 42.9g=___________ • 5.67 m x 13.44 m ___________ • (5.83 m/ 2.67 s) /2.1 s ___________ • 9.374 V x 6 ___________ 11.4 m/s 97.6 g 76.2 m2 1.0 m/s2 60 V From now on, we will round all our answers to the correct # of significant figures.

  11. EXTRA REVIEW • Using a calculator for EXPONONETS (EE, EXP or x10x button) • Example 1: (5.02 x 10-3) x (6.3369 x 105) = 3181.1238 *put in correct sig figs = 3 sig figs = 3180 or 3.18 x 103

  12. Example 2 (use EE button!) • (2.99 x 106) x (2.334 x 10-3) = = 6978.66 • 3 sig figs • 6980

  13. DIMENSIONAL ANALYSIS • How old are you in seconds? • Go from number of years to number of seconds. EX: 15 years old  _____ seconds old. To do this, you need to use CONVERSION FACTORS (a ratio of equivalent values used to express the same quantity in different units)

  14. Dimensional Analysis Performing these conversions is a lot like going on a road trip.

  15. ROAD TRIP!!! Let’s say you want to travel from Oracle Jct to Casa Grande... You must travel through Tucson… a two part trip.

  16. Rule: You must stay on the roads & REMEMBER SIG FIGS!!!

  17. DO NOT GO OFF ROAD!  X

  18. Rule: You need a map. Sometimes the map can be in your head. But, not at first. (show all work!!)

  19. GIVEN INFORMATION 1 kildurkin = 18 gallons 2 farkins = 1 kildurkin 1 hogshead = 63 gallons 1 barrel = 3.3 bushels 1 bushel = 8 gallons

  20. Make a UNIT CONVERSION MAP Draw connections between the units in the conversion factors… (as you draw connections, check that conversion factor off the list) It’s kind of like a road map…

  21. General Format... given going to = X coming from

  22. hogshead kildurkins farkins gallons barrel bushel

  23. Let’s calculate • Convert 14 gallons to kildurkins

  24. Convert 14 barrels to hogshead

  25. Convert 3.00 bushels to farkins

  26. Now you try one. How many farkins is 3.00 bushels? End Here hogshead kildurkins farkins gallons Start Here barrel bushel This will require 3 Conversions.

  27. farkins bushels gallons kildurkins 8.0 gallons 1.0 kildurkin 2.0 farkins 3.00 bushels X X X 1.0 bushel 18 gallons 1.0 kildurkin = 2.67 farkins

  28. Wow! How Cool Is That!

  29. Handout: Fun Factor Label • Handout • Piece of lined paper (landscape format) • Front is web for Distance and back is for Vol. • Conversion Factors: change 10-10 to 1 x 10-10 • Let’s do league  km  m  cm to start • You finish web, then do #3,6,7,9 • Then do vol. web • Then finish questions #4, 5, 8, 10 • FINISH FOR HW

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